Essential characteristics of noise

One of the major reasons for noise in an image is that the signal itself is noisy. Although this seems very far afield from photography, this is actually a direct consequence of quantum mechanics! The light falling onto the sensor is both an electromagnetic wave but also composed of particles—photons.

A finite number of photons hit a pixel within a given time interval. This is comparable to cars driving on a highway. Assume that the traffic flows at a constant pace and you count the cars passing under a gate in one minute. If you perform this experiment many times (under similar traffic conditions), then this number fluctuates around a mean value. This fluctuation is noise. Another point which is intuitive is that the SNR is lower for low observation time, because the flow of cars (or photons) is quantized. For very small pixel pitch (a few µm) and low exposure time, the quantization phenomenon becomes a major factor, as only about 1,000 photons can hit the pixel within the exposure time.

This source
of noise is called photonic noise, which is the main source of noise for
smaller pixel pitch. Another point worth noting is that photonic noise actually
increases with the signal. Indeed, if a pixel receives photons, then the standard
deviation of the noise is .

In a simplified model where all photons are converted into electrons, the number of incoming photons and the digital signal output are related by a multiplicative gain (either analog or digital), which is related to the ISO setting: high ISO means high gain.The noise standard deviation is amplified by the same gain factor. Let denote
this gain value. The sensor output ,
the number of photons ,
the gain ,
and the output noise are
related by

Therefore the
SNR is

Let’s consider different ISO settings such that the output gray level takes the same value. The SNR decreases with the gain, or equivalently, with the ISO settings. Multiplying the ISO setting by four implies that the SNR decreases by 2, which is a loss of 6dB, independent of the sensor. The rule of thumb is that doubling the ISO is a loss of 3dB. As a practical example, consider two cameras. The second camera has twice as many pixels as the first one for a same sensor size.

The lower figures represent the histogram of the gray level in a uniform patch of the target. With no noise, this histogram would be a perfect peak at a single value. The wider this histogram, the more noise in the image.

The mean reflectance of a natural scene is known to be about 18%. If the camera sets its exposure parameter to reach saturation on an object with a reflectance close to 100% (a “white” object), then the SNR 18% value is representative of the level of noise in the scene.